Tom,
The amplitudes of "overtones" or harmonics based on a fundamental
frequency are in principle completely arbitrary. Analysis of a
periodic signal waveform into a set of harmonic amplitudes and
phases is discussed in many books including the fifth chapter
entitled "Fourier Series" of
W. M. Hartmann, Signals, Sounds, and Sensation (Springer, 1998).
Now, if you are talking about musical instrument or vocal waveforms
this is a different story. In these cases, the harmonic amplitudes
are limited by the acoustics of the instrument in question. An old
book which contained graphs of many instrument harmonic amplitude
series (called "spectra") is
H. F. Olson, Music, Physics, and Engineering (Dover, 1952, 1967).
The graphs are mostly in Olson's Chapter six entitled
"Characteristics of Musical Instruments". These spectra should be
taken as typical but not all-inclusive because instrument spectra
depend on many factors such as instrument, player, fundamental
frequency, performance, room acoustics, and microphone placement.
These days you can find out the spectrum of an instrument by having
a player blow a tone into a computer and have the spectrum displayed
on the screen using a real-time analysis program. Several programs
of this type have been suggested on this list in the past.
Unfortunately, it seems that noone has yet published a complete corpus
of musical instrument spectra. Back in the 90's Gregory Sandell hosted
a website called SHARC which contained a pretty complete set of data
of this type. Unfortunately it seems that that site is dormant.
However, using the Univ. of Iowa samples
(http://theremin.music.uiowa.edu/MIS.html)
and a program such as SNDAN
(http://ems.music.uiuc.edu/beaucham/software/sndan/)
you can easily make your own data.
The percept most closely associated with the spectrum is called
timbre. Numerous studies have been published on aspects of timbre
in the Journal of the Acoustical Society and other journals and
some of these are discussed in various acoustics books.
Jim
James W. Beauchamp
Professor Emeritus of Music and Electrical & Computer Engineering
University of Illinois at Urbana-Champaign
2136 Music Bldg. MC-056
1114 W. Nevada, Urbana, IL 61801 USA
email: jwbeauch@xxxxxxxx (also: beaucham@xxxxxxxxxxxxxxxxxxxxxx)
phone: +1-217-344-3307 (also: 217-244-1207 and 217-333-3691)
fax: +1-217-344-3723 (also: 217-244-4585)
WWW: http://ems.music.uiuc.edu/beaucham
Original message:
> From: Tom Lee <edgar109@xxxxxxxxx>
> Date: Wed, 16 Nov 2005 16:58:35 -0800
> To: AUDITORY@xxxxxxxxxxxxxxx
> Subject: question about overtones
>
> Dear list,
>
> Does anyone have information about the amplitude
> relation between a tone and its overtones? What I mean
> is, if I have some frequency and I want to generate
> its natural overtone series, how loud do I make the
> overtones in relation to the fundamental? Thanks in advance!
>
> -Tom